Multi-digit+Division

Multi-digit Division: If you're ever stuck without a calculator
Multi-digit division isn't the focus of this course, but it often seems challenging for many students who are simply taught the standard procedure and asked to follow it without error, so this page describes an important alternative algorithm that most students should learn before (or instead of) the standard procedure. For that matter, students should not waste time and effort doing too many long divisions without the aid of a calculator. Once they get the idea shown below with two digit divisors, and understand the concept of multi-digit division, they can simply use a calculator, as adults do. More importantly, they should learn to make estimates of real-world division situations involving larger numbers.

The key to multi-digit division is the repeated subtraction method. As students get more practice with this, they become more proficient by making larger initial estimates. This helps with their ability to estimate the actual answer. Repeated subtraction is more error-free than the traditional algorithm for many students.

Here are two examples. The first one uses simple multipliers of 15. Think of this story as you look at it: A class has 390 cookies for a bake sale. They want to put 15 cookies on each plate. How many plates will they need? They guess 10 to start. But that's only 150 cookies. So there are 240 cookies left. They think, 10 more plates is another 150 cookies, leaving 90. Two more plates is 30, leaving 60 cookies... etc. As they do more of this, they figure out quickly that they don't have to repeatedly subtract by 2x. Or, they might make a table of simple multiples first, another approach.



In the second example, students can take away multiples of 10 if that's easier for them, until they see patterns emerge. But once someone shows them about taking half of 100 x 46 (in this case), they begin to get the idea of making larger estimates.